(1) Field of the Invention
The present invention is generally directed towards a method to measure the shear wavespeed in an isotropic plate. More specifically, the invention is directed towards a method to estimate the shear wavespeed of a plate shaped test specimen using a mechanical shaker test.
(2) Description of the Prior Art
The shear wave, S-wave or secondary wave, is one of the two main types of elastic body waves, a type of seismic wave, that moves through the body of an object, unlike surface waves. The shear wave moves as a shear or transverse wave, so motion is perpendicular or normal to the direction of wave propagation. The shear wave moves through elastic media, and the main restoring force comes from shear effects. These waves are divergenceless.
Measurement of material properties of elastic systems has been and continues to be an active area of investigation. Resonant techniques have been used that usually involve measuring the natural resonant frequencies of slender structures. Once measured, these frequencies are equated to the corresponding analytical natural frequencies, which are typically functions of Young's modulus, shear modulus, length and/or mass. The resultant expression can be solved, which produces an estimate of Young's or shear modulus at each natural frequency. Non-resonant methods have also been used. Although slightly more complicated than resonant techniques, these methods have the ability to estimate material properties at frequencies other than the natural frequency of the system. Typically, non-resonant techniques involve equating measured data with a simplified analytical model of the system. The analytical model is rewritten so that the material properties that are to be estimated are rendered as functions of the data.
Both resonant and non-resonant methods are usually performed at low frequencies, where simple (though limited) analytical models and corresponding dynamic behavior exists. Ideally, the structure under testing will have only a single mode of energy propagation, so that the effects of other wave motion will not corrupt the estimation process.
Few wavespeed estimation techniques have been developed for general plates and beams. Most of the research has assumed thin plate (or beam) behavior where the theory is that of a single flexural wave propagating in the structure. The estimation of Young's modulus and shear modulus have been accomplished by matching the theoretical eigen-frequencies of a Timoshenko beam model to measured data and then deducing the material parameters. Some techniques at ultrasonic frequencies have been derived, in order to support the medical imaging or the aviation industry. The measurement of elastic constants of thin immersed anisotropic plates has been undertaken using the identification of transmission zeros and poles based on various incident angles of an incoming ultrasonic wave. The estimation of stiffness and damping properties of viscoelastic materials by numerically inverting the transmitted ultrasonic field of an immersed thin plate at different incident angles has been accomplished.
A method has been devised to identify Lamé constants, thickness, density, longitudinal and shear attenuation and interfacial properties of a solid layer placed between two other layers. This method uses normal and angular ultrasonic reflectivity from the middle layer. The last three references involve modeling and measurement in the MHz region. Many indentation material testing methods exist. These usually consist of loading a location of the material and measuring the resultant force and depth. Using these measurements, one can determine Young's modulus and shear modulus. These methods are usually quasi-static and frequency independent.
The elastic plate theory has been extensively developed, though thick plates have traditionally not been used to measure material properties because they support multiple wave types, and any measurement technique has to have the ability to discern between each wave type and its contribution to the measurement. Transfer function methods that measure one output (at a single location) versus a fixed input do not have the capability to separate various wave types and their associated response levels.